Mean-Field Game Strategies for Optimal Execution
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Bibliographic record
Abstract
Algorithmic trading strategies for execution often focus on the individual agent who is liquidating/acquiring shares. When generalized to multiple agents, the resulting stochastic game is notoriously difficult to solve in closed-form. Here, we circumvent the difficulties by investigating a mean-field game framework containing (i) a major agent who is liquidating a large number of shares, (ii) a number of minor agents (high-frequency traders (HFTs)) who detect and trade against the liquidator, and (iii) noise traders who buy and sell for exogenous reasons. Our setup accounts for permanent price impact stemming from all trader types inducing an interaction between major and minor agents. Both optimizing agents trade against noise traders as well as one another. This stochastic dynamic game contains couplings in the price and trade dynamics, and we use a mean-field game approach to solve the problem. We obtain a set of decentralized feedback trading strategies for the major and minor agents, and express the solution explicitly in terms of a deterministic fixed point problem. For a finite N population of HFTs, the set of major-minor agent mean-field game strategies is shown to have a ϵN-Nash equilibrium property where ϵN→0 as N→∞.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it